Hi all,I am looking at implementing the Jarrow Yildirim model for the purpose of calculating Inflation on CVA. On first inspection, I see there are three processes - the nominal and real short rate processes and the Inflation Index process.Is it the case that only two out of the three of these processes need to be used for pricing Zero Coupon Swaps or Caps or am I missing something? Using the foreign currency analogy, one does not need to specify an IR process for each currency AND the a process for the FX rate, as, assuming Interest Rate Parity, only two of these processes are necessary.More generally, if I just wanted to simulate the nominal yield curve and the inflation index through time, I can just calibrate these two processes and ignore the real rate process? Or is it the case that if I then go to price YoY or LPI swaps from my simulations, my results will be far away from the market.

theoretically you only need either the nominal rate and inflation or real rates ... I am not sure how close to market prices you want to be as this is for CVA purposes and you are refining in the margins of error imho.

You should look at the Belgrade Benhamou and Koehler framework, where one deals only with nominal rates and inflation. It is a market model that is much more simple and intuitive (because it relies only on traded instruments) than JY, allowing to derive quickly convexity adjustment (YOY and payment delay) or structured pricing.

QuoteOriginally posted by: bazzatHi all,I am looking at implementing the Jarrow Yildirim model for the purpose of calculating Inflation on CVA. On first inspection, I see there are three processes - the nominal and real short rate processes and the Inflation Index process.Is it the case that only two out of the three of these processes need to be used for pricing Zero Coupon Swaps or Caps or am I missing something? Using the foreign currency analogy, one does not need to specify an IR process for each currency AND the a process for the FX rate, as, assuming Interest Rate Parity, only two of these processes are necessary.More generally, if I just wanted to simulate the nominal yield curve and the inflation index through time, I can just calibrate these two processes and ignore the real rate process? Or is it the case that if I then go to price YoY or LPI swaps from my simulations, my results will be far away from the market.Yes. For ZC Swaps and ZC Options you dont need a 3 factor model. At least not if you have enough quotes for the zc-options. For the YoY they behave like forward starting zc options. So they depend on the shape of the forward cuve on the time of resseting the earlier inflation fixing. That is when they enter into zc stage. Here it does matter if you assume a stochastic drift (implied by JY) or not (implied by simple BS with the Index as lognormal random variable)And the short answer is of course. Daveangel ist right. With CVA you might have other difficulties. Depends of course how liquid your conterparties trade (in cds terms) and how much you think about CVA hedging also.